Solve the system of equations.
6x–5y=27
3x+5y=36
To solve this system of equations, we can use the method of elimination. First, we'll add the two equations together to eliminate the y variable:
(6x - 5y) + (3x + 5y) = 27 + 36
9x = 63
Now we can solve for x by dividing both sides of the equation by 9:
9x/9 = 63/9
x = 7
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
6(7) - 5y = 27
42 - 5y = 27
Next, we'll move the constant term to the other side of the equation:
-5y = 27 - 42
-5y = -15
Finally, we'll divide both sides of the equation by -5 to solve for y:
y = -15 / -5
y = 3
So the solution to the system of equations is x = 7 and y = 3.
To solve this system of equations, we can use the method of elimination.
Step 1: Multiply both sides of the second equation by 2 to eliminate the y terms:
2 * (3x + 5y) = 2 * 36
6x + 10y = 72
Step 2: Add the first equation and the modified second equation:
(6x - 5y) + (6x + 10y) = 27 + 72
12x + 5y = 99
Step 3: Now we have a new equation: 12x + 5y = 99
Step 4: Solve the new equation for x:
12x = 99 - 5y
x = (99 - 5y) / 12
Step 5: Substitute the expression for x in the first equation:
6x - 5y = 27
6((99 - 5y) / 12) - 5y = 27
Step 6: Simplify the equation:
(99 - 5y) / 2 - 5y = 27
Step 7: Multiply through by 12 to eliminate the fraction:
99 - 5y - 60y = 324
Step 8: Combine like terms:
99 - 65y = 324
Step 9: Subtract 99 from both sides:
-65y = 225
Step 10: Divide both sides by -65:
y = -225 / 65
Step 11: Simplify the fraction:
y = -45 / 13
Step 12: Substitute the value of y into equation 1 to solve for x:
6x - 5(-45 / 13) = 27
Step 13: Simplify the equation:
6x + (225 / 13) = 27
Step 14: Subtract (225 / 13) from both sides:
6x = 27 - (225 / 13)
Step 15: Simplify the right side of the equation:
6x = (351 - 225) / 13
6x = 126 / 13
Step 16: Divide both sides by 6:
x = (126 / 13) / 6
Step 17: Simplify the expression:
x = 126 / (13 * 6)
Step 18: Reduce the fraction:
x = 7 / 13
So the solution to the system of equations is x = 7/13 and y = -45/13.
To solve the system of equations, you can use the method of elimination or substitution.
Let's use the method of elimination to solve this system.
First, add the two equations together to eliminate the 'y' variable:
(6x - 5y) + (3x + 5y) = 27 + 36
Combine like terms:
6x + 3x - 5y + 5y = 63
Simplify:
9x = 63
Divide both sides by 9:
x = 7
Now that we have the value of 'x', we can substitute it back into any of the original equations to find the value of 'y'. Let's substitute it into the first equation:
6x - 5y = 27
6(7) - 5y = 27
42 - 5y = 27
Subtract 42 from both sides:
-5y = 27 - 42
-5y = -15
Divide both sides by -5:
y = 3
So the solution to the system of equations is x = 7 and y = 3.